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Q.

A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force 2 N down the inclined plane. The maximum external force up the inclined plane that does not move the block is 10N. The coefficient of static friction between the block and the plane is : [ Take g = 10 $m / s^{2}$ ]

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a

$\frac{\sqrt{3}}{2}$

b

$\frac{\sqrt{3}}{4}$

c

$\frac{1}{2}$

d

$\frac{2}{3}$

answer is A.

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Detailed Solution

From figure,
$2 + m g \sin 30^{0} = μ m g \cos 30^{0} a n d 10 = m g \sin 30^{0} + μ m g \cos 30^{0} = 2 μ m g \cos 30^{0} - 2 \Rightarrow 6 = μ m g \cos 30^{0} a n d 4 = m g \cos 30^{0}$
By dividing above two $\Rightarrow \frac{3}{2} = μ \times \sqrt{3}$
Coefficient of friction, $μ = \frac{\sqrt{3}}{2}$

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A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force 2 N down the inclined plane. The maximum external force up the inclined plane that does not move the block is 10N. The coefficient of static friction between the block and the plane is : [ Take g = 10 m/s2 ]